Generative artificial intelligence (AI) has opened the possibility of automated content production, including coding in software development, which can significantly influence the participation and performance of software developers. To explore this impact, we investigate the role of GitHub Copilot, a generative AI pair programmer, on software development in open-source community, where multiple developers voluntarily collaborate on software projects. Using GitHub's dataset for open-source repositories and a generalized synthetic control method, we find that Copilot significantly enhances project-level productivity by 6.5%. Delving deeper, we dissect the key mechanisms driving this improvement. Our findings reveal a 5.5% increase in individual productivity and a 5.4% increase in participation. However, this is accompanied with a 41.6% increase in integration time, potentially due to higher coordination costs. Interestingly, we also observe the differential effects among developers. We discover that core developers achieve greater project-level productivity gains from using Copilot, benefiting more in terms of individual productivity and participation compared to peripheral developers, plausibly due to their deeper familiarity with software projects. We also find that the increase in project-level productivity is accompanied with no change in code quality. We conclude that AI pair programmers bring benefits to developers to automate and augment their code, but human developers' knowledge of software projects can enhance the benefits. In summary, our research underscores the role of AI pair programmers in impacting project-level productivity within the open-source community and suggests potential implications for the structure of open-source software projects.